Option a: [tex](-0.5,-1.75)[/tex] is the solution to the system of equations.
Explanation:
The equations are [tex]y=-\frac{2}{5} x-2[/tex] and [tex]y=5 x+1[/tex]
Equating these two equations, we have,
[tex]-\frac{2}{5} x-2=5 x+1[/tex]
Taking LCM and multiplying both sides by 5, we get,
[tex]-2 x-10=25 x+5[/tex]
Simplifying , we get,
[tex]\begin{aligned}-10-5 &=25 x+2 \\-15 &=27 x \\-\frac{15}{27} &=x \\-\frac{5}{9} &=x\end{aligned}[/tex]
Substituting the value of x in [tex]y=5 x+1[/tex], we get,
[tex]\begin{aligned}&y=5\left(-\frac{5}{9}\right)+1\\&y=-\frac{25}{9}+1\\&y=-\frac{16}{9}\end{aligned}[/tex]
Thus, the solution is [tex]\left(-\frac{5}{9},-\frac{16}{9}\right)[/tex]
Changing the solution from fraction to decimal, we get, [tex](-0.556,-1.778)[/tex]
Thus, the solution is [tex](-0.5,-1.75)[/tex]
Hence, option a is the correct answer.
